Business 90: Business Statistics Professor David Mease Sec 0 3 , T R 7 : 3 0- 8 : 4 5AM BBC 204

1. Business 90: Business Statistics Professor David Mease Sec 03, T R7:30-8:45AM BBC 204 Lecture 15 = Start Chapter “Some Important Discrete Probability Distributions” (SIDPD) Agenda: 1) Assign Homework 6 (due Tuesday 4/13) 2) Start Chapter SIDPD

2. Homework 6 – Due Tuesday 4/13 1) Read chapter entitled “Some Important Discrete Probability Distributions” but only sections 1-3. 2) In that chapter do textbook problems 3, 4, 14, 15 and 20 (but skip part g in 20) 3) Stock X has a mean of $50 and a standard deviation of $10. Stock Y has a mean of $100 and a standard deviation of $20. Find the mean and standard deviation of buying one share of each A) If they are independent (so the covariance is 0) B) If the covariance is 30 C) If the covariance is -30

3. Statistics for Managers Using Microsoft® Excel4th Edition Some Important Discrete Probability Distributions

4. Chapter Goals After completing this chapter, you should be able to: • Compute and interpret the mean and standard deviation for a discrete probability distribution • Explain covariance and its application in finance • Use the binomial probability distribution to find probabilities • Describe when to apply the binomial distribution

5. Introduction to Probability Distributions • Random Variable • Represents a possible numerical value from an uncertain event Random Variables Discrete Random Variable Continuous Random Variable (This Chapter) (Next Chapter)

6. Discrete Probability Distributions A discrete probability distribution is given by a table listing all possible values for the random variable along with the corresponding probabilities. The appropriate chart to display it is a bar chart (which has gaps, unlike a histogram).

7. In class exercise #58: A fair coin is tossed two times. Give the probability distribution and bar chart for the number of tails.

8. In class exercise #59: A fair coin is tossed three times. Give the probability distribution and bar chart for the number of tails.

9. In class exercise #60: A fair die is rolled once. Give the probability distribution and bar chart for the outcome.

10. In class exercise #61: A fair die is rolled twice. Give the probability distribution and bar chart for the total from the two rolls.

11. In class exercise #62: A fair die is rolled twice. Using your probability distribution from before answer the following: A) What is the probability that a seven is rolled? B) What is the probability that the roll is larger than 10? C) What is the probability that an even number is rolled? D) Given the roll is even, what is the probability it is a four? E) What is the probability the roll is even and four? F) What is the probability the roll is four or odd?

12. In class exercise #63: Many people toss a fair coin two times each. How many tails would you expect for each person on average?

13. Discrete Random Variable Summary Measures • Expected Value (or mean) of a discrete distribution (Weighted Average)

14. In class exercise #64: A box contains two $1 bills, one $5 bill and one $20 bill. You reach in without looking and pull out a single bill. Give the probability distribution and bar chart for the amount of money you pull out.

15. In class exercise #65: A box contains two $1 bills, one $5 bill and one $20 bill. Many people reach in without looking and each pull out a single bill and put it back. On average, how much money would you expect each person to get? How much money would you personally be willing to pay to play this game once?

16. In class exercise #66: A fair coin is to be tossed two times. A) Give the expected number of tails. B) Give the variance for the number of tails. C) Give the standard deviation for the number of tails.

17. Discrete Random Variable Summary Measures (continued) Variance of a discrete random variable Standard Deviation of a discrete random variable where: E(X) = Expected value of the discrete random variable X Xi = the ith outcome of X P(Xi) = Probability of the ith occurrence of X